Now, being FR curvature a quantity with a geometric basis, it does have the potential to provide insight about network properties. This is indeed the case, as experimental studies show that both in its plain [1]}, [2]}, and triangle-augmented [3]} versions, highly negative FR curvature is generally a good indicator that an edge is important for the network's structure. However, we would like to note that even if [3]} showed that both constructions of FR curvature seem to share this characteristic for real-world networks, it is quite easy to construct examples where their values greatly differ – see for example the network of Figure REF , where while every edge \(e^{\prime }\ne e\)  shows little variance between the two values, \(\mathcal {F}(e^{\prime }) = 1 - N\) , \(\mathcal {F}_\triangle (e^{\prime }) = 4 - N\) , the curvatures of edge \(e\)  are strikingly different: \(\mathcal {F}(e) = 2 - 2N\) , \(\mathcal {F}_\triangle (e) = 2 + N\) . In a similar fashion, one can build networks such that adding any specific term of [REF ] greatly modifies the value of the curvature of a single edge. As we will see, this type of discordance between plain and augmented curvature is not relegated to artificial networks, but can also be found in organic ones.
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